nuclear magnetic moments and electric quadrupole moments

Allan Adler

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no, scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>I\'ve been trying to make sense of Goeppert-Mayer\'s and Jenkins\' book\non the nuclear shell model, particularly the discussion in one appendix\nof the nuclear wave function for Li7, with spin 3/2 and isobaric spin 1/2.\nHere is something, probably easy, that I don\'t understand.\n\nSuppose you have an eigenfunction for m neutrons and n protons, each with\nassigned values of m_j, the eigenfunction being expressed as a Slater\ndeterminant. For example, one of the eigenfunctions for Li7 above is:\n\n|(pi psi^(3/2))(nu psi^(3/2))(nu psi^(-3/2))|\n\nFrom the computations of magnetic dipole moments and electric quadrupole\nmoments given in the same appendix, it seems that such Slater determinants\nare eigenfunctions for the operators needed to compute these moments.\nGiven such a Slater determinant, for m neutrons and n protons, how do\nyou write down its eigenvalue for the magnetic dipole moment and electric\nquadrupole moment?\n--\nIgnorantly,\nAllan Adler <ara@zurich.csail.mit.edu>\n* Disclaimer: I am a guest and *not* a member of the MIT CSAIL. My actions and\n* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>I've been trying to make sense of Goeppert-Mayer's and Jenkins' book
on the nuclear shell model, particularly the discussion in one appendix
of the nuclear wave function for Li7, with spin 3/2 and isobaric spin 1/2.
Here is something, probably easy, that I don't understand.

Suppose you have an eigenfunction for m neutrons and n protons, each with
assigned values of [itex]m_j,[/itex] the eigenfunction being expressed as a Slater
determinant. For example, one of the eigenfunctions for Li7 above is:

[tex]|(\pi \psi^(3/2))(\nu \psi^(3/2))(\nu \psi^(-3/2))|[/tex]

From the computations of magnetic dipole moments and electric quadrupole
moments given in the same appendix, it seems that such Slater determinants
are eigenfunctions for the operators needed to compute these moments.
Given such a Slater determinant, for m neutrons and n protons, how do
you write down its eigenvalue for the magnetic dipole moment and electric
quadrupole moment?
--
Ignorantly,
Allan Adler <ara@zurich.csail.mit.edu>
* Disclaimer: I am a guest and [itex]*not* a[/itex] member of the MIT CSAIL. My actions and
* comments do not reflect in any way on MIT. Also, I am nowhere near Boston.

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